XMS SEC 4 EMATH 2022 WA1

3 1 On each of the Venn diagrams, shade the region represented by the set notation. (a) P′ Q [1] (b) A′ ( )AB [1] 2 Write down the set notation that represents the shaded region in the Venn diagrams as shown below. (a) Answer …………………….. [1] P Q A B  Q P [Turn over

4 (b) Answer …………………….. [1] 3 It is given that  , , , , , ,X a b c d e f g= and  , , ,Y a b d g= . (a) Draw a Venn diagram to represent sets X and Y. [1] (b) Is Y a proper subset of X ? Explain. …………………………………………………………………………………… …………………………………………………………………………………… ……………………………………………………………………………… [1]  A B

5 4 It is given that  = {x : x is an integer such that 1  x < 15}, A = {x : x is an odd number} and B = {x : x is a multiple of 3}. (a) Illustrate the given information using a Venn diagram. [2] (b) List the elements in the set A B′. Answer …………………………………………………….. [1] (c) Find n (A B)′. Answer …………………….. [1] (d) A number a is chosen at random from  . Find the probability that ( )a A B . Answer …………………….. [1] [Turn over

6 5 Amy has 40 red balls, x yellow balls and (3x – 8) blue balls in a bag. She selects a ball from the bag at random. Given that the probability of a yellow ball being selected is 1 5 , find (a) the value of x, Answer x = ……………………. [2] (b) the probability of selecting a red or blue ball from the bag. Answer ……………………..…. [1]

7 6 In a school examination, the probabilities that Daisy will pass Mathematics, English and Science are 7 8 , 7 10 and 4 5 respectively. Find the probability that Daisy (a) passes Science only, Answer ……………………..…. [2] (b) fails exactly two subjects, Answer ……………………..…. [2] (c) passes at least one subject. Answer ……………………..…. [2] [Turn over

8 7 A bag contains 6 blue, 5 green and 7 yellow marbles. A child is allowed to pick two marbles from the bag, one after another without replacement. (a) Complete the tree diagram below. [2] (b) Find the probability that the two marbles picked are (i) of the same colour, Answer ……………………..…. [2] 1st Blue Green Yellow       2nd Blue Green Yellow Blue Green Yellow Blue Green Yellow

9 (ii) exactly one green and one yellow, Answer ……………………..…. [2] (iii) not green. Answer ……………………..…. [2] (c) If a third marble is picked, find the probability that all three marbles are